Im actually surprised that site presents counter arguments to their own claim. They state:
"A good possibility is that solidification of magma does not reset the radioisotope clock to zero. Probably some argon-40 is incorporated from the start into newly formed minerals giving the "appearance" of great age. "
Which is the first thing that popped into my head. Where's the literature describing the effects of state transformation of the atomic composition of lava? You cannot assume the rock is "new" just because it turned solid.